Effects of Homogeneous–Heterogeneous Reactions on the Viscoelastic Fluid Toward a Stretching Sheet

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
W. A. Khan ◽  
I. M. Pop
Keyword(s):  
Boundary Layer ◽  
Viscoelastic Fluid ◽  
Diffusion Coefficients ◽  
Stretching Sheet ◽  
Equations Of Motion ◽  
Heterogeneous Reactions ◽  
Viscoelastic Parameter ◽  
Implicit Finite Difference ◽  
Layer Flow ◽  
Basic Boundary

The effects of homogeneous–heterogeneous reactions on the steady viscoelastic fluid toward a stretching sheet are numerically investigated in this paper. The model developed by Chaudhary and Merkin for homogeneous–heterogeneous reactions in stagnation-point boundary-layer flow with equal diffusivities for reactant and autocatalyst is used for present stretching sheet problem in a viscoelastic fluid. The basic boundary layer partial differential equations of motion and concentration are reduced to ordinary differential (similarity) equations, which then are numerically solved using an implicit finite difference method in the case when the diffusion coefficients of both reactant and autocatalyst are equal. It is found that the concentration at the surface decreases with an increase in the viscoelastic parameter and strengths of the homogeneous, while heterogeneous reactions increase.

scholarly journals Analysis of Boundary Layer Flow and Heat Transfer for two Classes of Viscoelastic Fluid Over a Stretching Sheet with Heat Generation or Absorption

1970 ◽  
Vol 46 (4) ◽  
pp. 451-456 ◽  
Author(s):  
K Bhattacharyya ◽  
MS Uddin ◽  
GC Layek ◽  
W Ali Pk
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Second Grade ◽  
Grade Fluid ◽  
Heat Generation Or Absorption ◽  
Layer Flow

In this paper, we obtained solutions of boundary layer flow and heat transfer for two classes of viscoelastic fluid over a stretching sheet with internal heat generation or absorption. In the analysis, we consider second-grade fluid and Walter's liquid B. The governing equations are transformed into self-similar ordinary differential equations by similarity transformations. The flow equation relating to momentum is solved analytically and then the heat equation using the Kummer's function. The analysis reveals that for the increase in magnitude of viscoelastic parameter both the velocity and temperature for a fixed point increase for second-grade fluid and both decrease for Walter's liquid B. Due to increase in Prandtl number and heat sink parameter, the thermal boundary layer thickness reduces, whereas increasing heat source parameter increases that thickness. Key words: Boundary layer flow; Heat transfer; Viscoelastic fluid; Stretching sheet; Heat generation or absorption DOI: http://dx.doi.org/10.3329/bjsir.v46i4.9590 BJSIR 2011; 46(4): 451-456

Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow of a Maxwell Nanofluid Over a Stretching Surface

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Nai-Li Xu ◽  
Hang Xu
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Shooting Method ◽  
Flow Direction ◽  
Equations Of Motion ◽  
Maxwell Fluid ◽  
Heterogeneous Reactions ◽  
Physical Parameters ◽  
Layer Flow ◽  
The Stability

Based on Buongiorno's theory and Cauchy equations of motion, a model is developed to examine homogeneous–heterogeneous reactions in boundary layer flow of a nanofluid over a stretching sheet in which a uniform magnetic field is added perpendicular to the flow direction. We apply the shooting method and the fourth-order Runge–Kutta integration to obtain multiple solutions of nonlinear ordinary differential equations with various physical parameters. Results show that nanofluids play significant roles in the procedures of homogeneous and heterogeneous reactions, which may help maintain the stability of chemical reactions. In addition, the terms related to Maxwell fluid either have effect on stability of the system; furthermore, the increasing elastic and magnetic parameters delay the appearance of bifurcation points.

scholarly journals Magnetohydrodynamic Boundary Layer Flow of a Viscoelastic Fluid Past a Nonlinear Stretching Sheet in the Presence of Viscous Dissipation Effect

Coatings ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 490
Author(s):  
Ahmad Banji Jafar ◽  
Sharidan Shafie ◽  
Imran Ullah
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Viscoelastic Fluid ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Dissipation Effect ◽  
Layer Flow ◽  
Nonlinear Stretching

This paper numerically investigates the viscous dissipation effect on the boundary layer flow of an electrically-conducting viscoelastic fluid (Walter’s B liquid) past a nonlinear stretching sheet. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. The transformed equations are then solved using the Keller box method. A careful evaluation of the influence of the pertinent parameters on the velocity field and temperature distributions through various plots is done for the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. The computed coefficient of skin friction, the rate of heat transfer (Nusselt number), and the temperature at the wall are also presented in tabular form. It is revealed from this table that the magnitude of the heat transfer is reduced with the increase in the Eckert number E c , viscoelastic parameter K, and magnetic parameter M for the PST case by about 12%, 20%, and 29%, respectively. Similarly, the temperature at the wall for the PHF case also decreases with the increase in E c and M by about 8% and 24%, respectively. It is obvious that the application of the PST condition excels at keeping the viscoelastic fluid warmer than the PHF condition. This implies that applying the PHF condition is better for cooling the sheet faster. The temperature at the wall is unchanged with the changes in the pertinent parameters in the PST case, and it is ascertained that the present results are in close agreement with the previous published results.

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